Abelian variety search results

Base field	Base char.	Dimension	$p$-rank	Initial coefficients
Simple	Geom. simple	Primitive	Princ. polarizable	Jacobian
Slopes	Points on variety	Points on curve	Simple factors
Angle rank	# Jacobians	# Hyp. Jacobians	# twists	Max twist degree
End. degree	$p$-rank deficit	(Geom.) Sq.free
Use Geometric decomposition in the following inputs
Dim 1 factors	Dim 2 factors	Dim 3 factors	Dim 4 factors	Dim 5 factors
(distinct)	(distinct)	(distinct)	Number field	Galois group

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Results (1-50 of 135930 matches)

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Label	Dimension	Base field	Base char.	L-polynomial	$p$-rank	$p$-rank deficit	points on curve	points on variety	Isogeny factors
1.5.ae	$1$	$\F_{5}$	$5$	$1 - 4 x + 5 x^{2}$	$1$	$0$	$2$	$2$	simple
1.5.ad	$1$	$\F_{5}$	$5$	$1 - 3 x + 5 x^{2}$	$1$	$0$	$3$	$3$	simple
1.5.ac	$1$	$\F_{5}$	$5$	$1 - 2 x + 5 x^{2}$	$1$	$0$	$4$	$4$	simple
1.5.ab	$1$	$\F_{5}$	$5$	$1 - x + 5 x^{2}$	$1$	$0$	$5$	$5$	simple
1.5.a	$1$	$\F_{5}$	$5$	$1 + 5 x^{2}$	$0$	$1$	$6$	$6$	simple
1.5.b	$1$	$\F_{5}$	$5$	$1 + x + 5 x^{2}$	$1$	$0$	$7$	$7$	simple
1.5.c	$1$	$\F_{5}$	$5$	$1 + 2 x + 5 x^{2}$	$1$	$0$	$8$	$8$	simple
1.5.d	$1$	$\F_{5}$	$5$	$1 + 3 x + 5 x^{2}$	$1$	$0$	$9$	$9$	simple
1.5.e	$1$	$\F_{5}$	$5$	$1 + 4 x + 5 x^{2}$	$1$	$0$	$10$	$10$	simple
2.5.ai_ba	$2$	$\F_{5}$	$5$	$( 1 - 4 x + 5 x^{2} )^{2}$	$2$	$0$	$-2$	$4$	1.5.ae^2
2.5.ah_w	$2$	$\F_{5}$	$5$	$( 1 - 4 x + 5 x^{2} )( 1 - 3 x + 5 x^{2} )$	$2$	$0$	$-1$	$6$	1.5.ae $\times$ 1.5.ad
2.5.ag_r	$2$	$\F_{5}$	$5$	$1 - 6 x + 17 x^{2} - 30 x^{3} + 25 x^{4}$	$2$	$0$	$0$	$7$	simple
2.5.ag_s	$2$	$\F_{5}$	$5$	$( 1 - 4 x + 5 x^{2} )( 1 - 2 x + 5 x^{2} )$	$2$	$0$	$0$	$8$	1.5.ae $\times$ 1.5.ac
2.5.ag_t	$2$	$\F_{5}$	$5$	$( 1 - 3 x + 5 x^{2} )^{2}$	$2$	$0$	$0$	$9$	1.5.ad^2
2.5.af_n	$2$	$\F_{5}$	$5$	$1 - 5 x + 13 x^{2} - 25 x^{3} + 25 x^{4}$	$2$	$0$	$1$	$9$	simple
2.5.af_o	$2$	$\F_{5}$	$5$	$( 1 - 4 x + 5 x^{2} )( 1 - x + 5 x^{2} )$	$2$	$0$	$1$	$10$	1.5.ae $\times$ 1.5.ab
2.5.af_p	$2$	$\F_{5}$	$5$	$1 - 5 x + 15 x^{2} - 25 x^{3} + 25 x^{4}$	$0$	$2$	$1$	$11$	simple
2.5.af_q	$2$	$\F_{5}$	$5$	$( 1 - 3 x + 5 x^{2} )( 1 - 2 x + 5 x^{2} )$	$2$	$0$	$1$	$12$	1.5.ad $\times$ 1.5.ac
2.5.ae_i	$2$	$\F_{5}$	$5$	$1 - 4 x + 8 x^{2} - 20 x^{3} + 25 x^{4}$	$2$	$0$	$2$	$10$	simple
2.5.ae_j	$2$	$\F_{5}$	$5$	$1 - 4 x + 9 x^{2} - 20 x^{3} + 25 x^{4}$	$2$	$0$	$2$	$11$	simple
2.5.ae_k	$2$	$\F_{5}$	$5$	$( 1 - 4 x + 5 x^{2} )( 1 + 5 x^{2} )$	$1$	$1$	$2$	$12$	1.5.ae $\times$ 1.5.a
2.5.ae_l	$2$	$\F_{5}$	$5$	$1 - 4 x + 11 x^{2} - 20 x^{3} + 25 x^{4}$	$2$	$0$	$2$	$13$	simple
2.5.ae_m	$2$	$\F_{5}$	$5$	$1 - 4 x + 12 x^{2} - 20 x^{3} + 25 x^{4}$	$2$	$0$	$2$	$14$	simple
2.5.ae_n	$2$	$\F_{5}$	$5$	$( 1 - 3 x + 5 x^{2} )( 1 - x + 5 x^{2} )$	$2$	$0$	$2$	$15$	1.5.ad $\times$ 1.5.ab
2.5.ae_o	$2$	$\F_{5}$	$5$	$( 1 - 2 x + 5 x^{2} )^{2}$	$2$	$0$	$2$	$16$	1.5.ac^2
2.5.ad_e	$2$	$\F_{5}$	$5$	$1 - 3 x + 4 x^{2} - 15 x^{3} + 25 x^{4}$	$2$	$0$	$3$	$12$	simple
2.5.ad_f	$2$	$\F_{5}$	$5$	$1 - 3 x + 5 x^{2} - 15 x^{3} + 25 x^{4}$	$1$	$1$	$3$	$13$	simple
2.5.ad_g	$2$	$\F_{5}$	$5$	$( 1 - 4 x + 5 x^{2} )( 1 + x + 5 x^{2} )$	$2$	$0$	$3$	$14$	1.5.ae $\times$ 1.5.b
2.5.ad_h	$2$	$\F_{5}$	$5$	$1 - 3 x + 7 x^{2} - 15 x^{3} + 25 x^{4}$	$2$	$0$	$3$	$15$	simple
2.5.ad_i	$2$	$\F_{5}$	$5$	$1 - 3 x + 8 x^{2} - 15 x^{3} + 25 x^{4}$	$2$	$0$	$3$	$16$	simple
2.5.ad_j	$2$	$\F_{5}$	$5$	$1 - 3 x + 9 x^{2} - 15 x^{3} + 25 x^{4}$	$2$	$0$	$3$	$17$	simple
2.5.ad_k	$2$	$\F_{5}$	$5$	$( 1 - 3 x + 5 x^{2} )( 1 + 5 x^{2} )$	$1$	$1$	$3$	$18$	1.5.ad $\times$ 1.5.a
2.5.ad_l	$2$	$\F_{5}$	$5$	$1 - 3 x + 11 x^{2} - 15 x^{3} + 25 x^{4}$	$2$	$0$	$3$	$19$	simple
2.5.ad_m	$2$	$\F_{5}$	$5$	$( 1 - 2 x + 5 x^{2} )( 1 - x + 5 x^{2} )$	$2$	$0$	$3$	$20$	1.5.ac $\times$ 1.5.ab
2.5.ac_ab	$2$	$\F_{5}$	$5$	$1 - 2 x - x^{2} - 10 x^{3} + 25 x^{4}$	$2$	$0$	$4$	$13$	simple
2.5.ac_a	$2$	$\F_{5}$	$5$	$1 - 2 x - 10 x^{3} + 25 x^{4}$	$1$	$1$	$4$	$14$	simple
2.5.ac_b	$2$	$\F_{5}$	$5$	$1 - 2 x + x^{2} - 10 x^{3} + 25 x^{4}$	$2$	$0$	$4$	$15$	simple
2.5.ac_c	$2$	$\F_{5}$	$5$	$( 1 - 4 x + 5 x^{2} )( 1 + 2 x + 5 x^{2} )$	$2$	$0$	$4$	$16$	1.5.ae $\times$ 1.5.c
2.5.ac_d	$2$	$\F_{5}$	$5$	$1 - 2 x + 3 x^{2} - 10 x^{3} + 25 x^{4}$	$2$	$0$	$4$	$17$	simple
2.5.ac_e	$2$	$\F_{5}$	$5$	$1 - 2 x + 4 x^{2} - 10 x^{3} + 25 x^{4}$	$2$	$0$	$4$	$18$	simple
2.5.ac_f	$2$	$\F_{5}$	$5$	$1 - 2 x + 5 x^{2} - 10 x^{3} + 25 x^{4}$	$1$	$1$	$4$	$19$	simple
2.5.ac_g	$2$	$\F_{5}$	$5$	$1 - 2 x + 6 x^{2} - 10 x^{3} + 25 x^{4}$	$2$	$0$	$4$	$20$	simple
2.5.ac_h	$2$	$\F_{5}$	$5$	$( 1 - 3 x + 5 x^{2} )( 1 + x + 5 x^{2} )$	$2$	$0$	$4$	$21$	1.5.ad $\times$ 1.5.b
2.5.ac_i	$2$	$\F_{5}$	$5$	$1 - 2 x + 8 x^{2} - 10 x^{3} + 25 x^{4}$	$2$	$0$	$4$	$22$	simple
2.5.ac_j	$2$	$\F_{5}$	$5$	$1 - 2 x + 9 x^{2} - 10 x^{3} + 25 x^{4}$	$2$	$0$	$4$	$23$	simple
2.5.ac_k	$2$	$\F_{5}$	$5$	$( 1 - 2 x + 5 x^{2} )( 1 + 5 x^{2} )$	$1$	$1$	$4$	$24$	1.5.ac $\times$ 1.5.a
2.5.ac_l	$2$	$\F_{5}$	$5$	$( 1 - x + 5 x^{2} )^{2}$	$2$	$0$	$4$	$25$	1.5.ab^2
2.5.ab_af	$2$	$\F_{5}$	$5$	$1 - x - 5 x^{2} - 5 x^{3} + 25 x^{4}$	$1$	$1$	$5$	$15$	simple
2.5.ab_ae	$2$	$\F_{5}$	$5$	$1 - x - 4 x^{2} - 5 x^{3} + 25 x^{4}$	$2$	$0$	$5$	$16$	simple
2.5.ab_ad	$2$	$\F_{5}$	$5$	$1 - x - 3 x^{2} - 5 x^{3} + 25 x^{4}$	$2$	$0$	$5$	$17$	simple

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